12/x+12=x+4/x+20

Solution for 12/x+12=x+4/x+20 equation:

12/x+12=x+4/x+20

We move all terms to the left:

12/x+12-(x+4/x+20)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+20)!=0

x∈R


We get rid of parentheses

12/x-x-4/x-20+12=0

We multiply all the terms by the denominator


-x*x-20*x+12*x+12-4=0

We add all the numbers together, and all the variables

-8x-x*x+8=0

Wy multiply elements

-1x^2-8x+8=0

a = -1; b = -8; c = +8;
Δ = b2-4ac
Δ = -82-4·(-1)·8
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*-1}=\frac{8-4\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*-1}=\frac{8+4\sqrt{6}}{-2}
$